Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?(1 point)

Question

Responses

The only outlier of the dataset is 16.
The only outlier of the dataset is 16.

There are no outliers in the dataset.
There are no outliers in the dataset.

The outliers of the dataset are 14 and 16.
The outliers of the dataset are 14 and 16.

The outliers of the dataset are 5, 14, and 16.

Answer 1

To determine the outliers in the dataset \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \), we can use the interquartile range (IQR) method.

1. Calculate Q1 and Q3:

   • Arrange the data: \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \)
   • The median (Q2) is the average of the 6th and 7th values: \( \frac{8 + 8}{2} = 8 \).
   • Q1 (the median of the first half \( 5, 6, 6, 7, 7 \)) = 6.
   • Q3 (the median of the second half \( 8, 8, 9, 9, 14, 16 \)) = \( \frac{9 + 14}{2} = 11.5 \).

2. Calculate the IQR:

   • \( IQR = Q3 - Q1 = 11.5 - 6 = 5.5 \)

3. Determine outlier boundaries:

   • Lower boundary = \( Q1 - 1.5 \times IQR = 6 - 1.5 \times 5.5 = 6 - 8.25 = -2.25 \)
   • Upper boundary = \( Q3 + 1.5 \times IQR = 11.5 + 1.5 \times 5.5 = 11.5 + 8.25 = 19.75 \)

4. Identify outliers:

   • Any data point less than -2.25 or greater than 19.75 is considered an outlier in this dataset.
   • The values in the dataset are \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \), and all are within the boundaries.

Based on these calculations, we can conclude that there are no outliers in the dataset.

The correct response is: There are no outliers in the dataset.